+1 Equipment is very definitely still 'magic' in 5e, and it's not 'common' - it's uncommon for weapons and rare for armour (Masterwork equipment is Pathfinder thing). A +1 with bonus extra effect as well usually jumps up a rarity grade - so a +2 weapon with a strong bonus damage component might end up falling into the very rare or even legendary category, depending on the extra effect, for example.
What is worth mentioning is that there are some more common magic weapon enchantments that are in the 'common' bracket - and they're quite nice because despite being effectively a "+0" weapon, they still count as magical for the purposes of cutting through damage resistance and so on. A weapon of Warning is a good example of a very useful common magic weapon. A lot of DMs that run high magic worlds with magic smiths and arcanists in major locations often offer basic magical enchantments at a cheap price not much higher than silvering; making a non magic weapon into a magic one, such that it doesn't get any bonuses of buffs, but not is enchanted and is magical for damage purposes. To be clear - the Sword Coast is generally considered a high magic setting, and while world building depends on individual DMs, such would not be uncommon in major locations, like Waterdeep or Neverwinter, etc.
The other thing that I feel is worthwhile pointing to for this discussion is the DMG's guide for creating and placing magic items into your game; yes, you might have rolled a +1 weapon on the loot table, but that doesn't mean it has to be boring. the DMG has a few lists and tables designed specifically to add flavour and minor properties to magic items to make them unique and fun, even if the base weight of their value is in a simple, generic enchantment. These tables contain story and rp hooks, such as the make and original crafters of the item, aesthetic flavour elements for character, but also traits and oddities - such as needing blood to activate, fast attunement, morphic shape or appearance, maybe it helps you swim better, or grants a small bonus to initiative, sheds light under certain circumstances, or always shows you where north is... and these tables are just suggestions for the sorts of things that you can characterise a 'bland' +1 weapon with to make it more interesting, or even to tie it into the setting.
One example: I once had a cloak of protection roll up as the reward for a bard player... Now I could have given them this:
Cloak of Protection
Wondrous Item, Uncommon
(Requires Attunement)
You gain +1 to your AC and all Saving Throws while wearing this cloak.
I gave them this instead:
Cloak of Fermatas
Wondrous Item, Uncommon
(Requires Attunement)
This cloak is of elven make, in dark green hues with silver thread picking out the patterns of covering leaves stitched to look like armour scales. It has almost no weight to it, but when wearing it you feel subtlety more confident in your actions and decisions. When the cloak is struck by any kind of hostile force, the silver threading lights up in patterns that reveal a network of musical notes and bars, hidden throughout the leaf designs, and you hear faint strains of ancient music in your mind. You gain +1 to your AC and all Saving Throws while wearing this cloak.
It's the same item, it's just had some minor properties and details thrown onto it, some of which can serve as rp hooks, some of which could lead to story exploration if the player gets invested in it, and some of which simply add flavour and character - its design and crafting origin, and so on. The properties were all derived (with slight tweaking) from the customisation tables in the DMG, to liven up a mundane magic item.
I'd like a decent scattering of interesting and unique equipment - even if its core effect is just a +1 or something otherwise mundane.
